We shall collect some useful information on modified Bessel functions. For more details we refer to [1]}, [2]}.
We define first the Bessel functions of order \(\nu \in \mathbb {C}\)  by
\(J_{\nu }(z)=\sum _{m=0}^{\infty }\frac{(-1)^{m}\left(\frac{z}{2}\right)^{\nu +2m}}{m!\Gamma (\nu +m+1)},\quad |\mbox{arg}(z)|<\pi .\) 
